Mathematics, 28.06.2019 00:20 jbarbie3

Solve the equation for x. if a solution is extraneous, be sure to identify it on your final answer.
square root x + 6 - 4 = x

Solve the equation for x. if a solution is extraneous, be sure to identify it on your final answer.

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Answer from: alex43079

The solutions to the equation $\sqrt{x+6}-4=x$ are x = -5 or x = -2.

Further Explanation:

We first isolate the square root. To do this, we cancel the 4 by adding it to each side:

$\sqrt{x+6}-4+4=x+4\\\\\sqrt{x+6}=x+4$

Next we want to cancel the square root sign. To do this, we square both sides of the equation:

$(\sqrt{x+6})^2=(x+4)^2\\\\x+6=(x+4)(x+4)\\\\x+6=x(x)+4(x)+4(x)+4(4)\\\\x+6=x^2+4x+4x+16\\\\x+6=x^2+8x+16$

Now we want to gather all of the variables on one side of the equation. The simplest way to do this will be to subtract x from each side:

$x+6-x=x^2+8x+16-x\\\\6=x^2+7x+16$

To solve quadratic equations (those with an x² term), we want ot set them equal to 0. To do this, we subtract 6 from each side:

$6-6=x^2+7x+16-6\\\\0=x^2+7x+10$

We can now factor the right hand side of the equation. To do this, we find factors of the constant, 10, that sum to the x term, 7. Looking at all of the factors of 10, we see that 5 and 2 have a sum of 7; this gives us

0=(x+5)(x+2)

Using the zero product property, we know that in order to have a product of 0, one or more of the factors must be equal to 0. This tells us that we have

$x+5=0\text{ or }x+2=0$

To solve the first equation, we subtract 5 from each side:

$x+5-5=0-5\\\\x=-5$

To solve the second equation, we subtract 2 from each side:

$x+2-2=0-2\\\\x=-2$

This means the solutions are x = -5 or x = -2.

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Keywords: radical equation, identify extraneous solution, square root equation

Answer from: Quest

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction: this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology: the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion: the last is the discussion, this can be either by management people or persons who are all interested , etc.

Answer from: Quest

first one because it can't have a fraction in it

step-by-step explanation:

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